Sabrent Thunderbolt 3 Enclosure cannot be recognised anymore

Yes and maybe. With almost every macOS 12.x Monterey update people have been reporting compatibility issues with various external devices. Added to the complication is what file system is being used on the external drive. People using NTFS on the external drives have seen macOS updates/upgrades break the third party NTFS drivers so it is best to only use a file system natively supported by macOS (HFS+, APFS, exFAT). When testing the external drive make sure to disconnect all unnecessary devices in case one of them is interfering with the external SSD. Try booting into Safe Mode to see whether you have the same issues. If Safe Mode works, then you have some third party software that is interfering.

As for moving the SSD to another enclosure it will depend on whether the failure is due to a compatibility issue or hardware issue with the enclosure, or if the SSD is failing or having issues. I used a Sabrent USB enclosure many years ago and was not impressed, but maybe they've gotten better over the years, although I know reviewers do like the Sabrent SSD bare drive performance (unfortunately most reviewers don't really review more than how fast a drive is these days and skip reliability, etc.). OWC makes good enclosures (Mercury Elite?), although I don't like the fact those enclosures don't allow access to the drive's health information, although many SSDs today don't have a lot of health information available. I personally like the Plugable brand and have used StarTech a lot in the past as well.

I did provide a link to the instructions for accessing Safe Mode in my previous post (a blue hyperlink in my first reference to Safe Mode). Here is the link again:

How to use safe mode on your Mac - Apple Support

You can try checking the health of the SSD by running DriveDx. You will need to install a special USB driver to attempt to access the health information on the external SSD. However, even with the special USB driver some USB chipsets in adapters/docks/enclosures will not allow the necessary communication to access the SSDs health information. Post the complete DriveDx text report here using the "Additional Text" icon which looks like a piece of paper. These types of apps may show "warning" or "failing" notices which may not be anything to worry about -- SSDs really need to have their health information manually inspected & interpreted to determine if those notices are a concern. Plus sometimes the health report may show a problem that does not trigger any warning or failing notices.

I think using an enclosure from any of the brands I listed will be fine. When buying from OWC I prefer their aluminum enclosures since the plastic ones seem to be lower quality all around. I'm sure there are some other brands than the ones I listed which are just as good.